function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta


J = (-1/m)*(y'*log(sigmoid(X*theta))+(ones(m,1)-y)'*log(ones(m,1)-sigmoid(X*theta)))+(0.5*lambda/m)*theta(2:end)'*theta(2:end);
grad(1)=(1/m)*((sigmoid(X*theta)-y)'*X(1:end,1));
grad(2:end) = (1/m)*((sigmoid(X*theta)-y)'*X(1:end,2:end))'+(lambda/m)*theta(2:end);



% =============================================================

end
